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I'm assuming stable wormhole really exist (naturally/microscopic or not) how can we distinguish between a wormhole and a black hole since we can't probe their "insides"?

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    $\begingroup$ The exotic matter around a traversable wormhole should give it away. $\endgroup$ – CuriousOne Jan 6 '16 at 1:00
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This is a from Cornell University Library, hopefully you can delve more into it for your answer.

Distinguishing black holes and wormholes with orbiting hot spots

Zilong Li, Cosimo Bambi

(Submitted on 8 May 2014 (v1), last revised 25 Jul 2014 (this version, v2))

The supermassive black hole candidates at the center of every normal galaxy might be wormholes created in the early Universe and connecting either two different regions of our Universe or two different universes in a Multiverse model. Indeed, the origin of these supermassive objects is not well understood, topological non-trivial structures like wormholes are allowed both in general relativity and in alternative theories of gravity, and current observations cannot rule out such a possibility. In a few years, the VLTI instrument GRAVITY will have the capability to image blobs of plasma orbiting near the innermost stable circular orbit of SgrA∗, the supermassive black hole candidate in the Milky Way. The secondary image of a hot spot orbiting around a wormhole is substantially different from that of a hot spot around a black hole, because the photon capture sphere of the wormhole is much smaller. The radius of the photon capture sphere is independent of the hot spot model, and therefore its possible detection, which is observationally challenging but not out of reach, can unambiguously test if the center of our Galaxy harbors a wormhole rather than a black hole.

Comments: 11 pages, 4 figures. v2: refereed version Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Astrophysical Phenomena (astro-ph.HE) Journal reference: Phys. Rev. D 90, 024071 (2014) DOI: 10.1103/PhysRevD.90.024071 Cite as: arXiv:1405.1883 [gr-qc]

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